# Simplifying Variable Expressions

Learn the definition of variable and expression and how to simplify variable expressions.

## Step by step guide to simplifying variable expressions

• In algebra, a variable is a letter used to stand for a number. The most common letters are: $$x, y, z, a, b, c, m$$ and $$n$$.
• An algebraic expression is an expression contains integers, variables, and math operations such as addition, subtraction, multiplication, division, etc.
• In an expression, we can combine “like” terms. (values with same variable and same power)

### Example 1:

Simplify this expression. $$2 \ x \ + \ 3 \ x \ + \ 4=$$?

Solution:

Combine “like” terms. Then: $$2 \ x \ + \ 3 \ x \ = 5 \ x$$ (remember you cannot combine variables and numbers).

Then: $$2 \ x \ + \ 3 \ x \ + \ 4=5 \ x \ + \ 4$$ (remember you cannot combine variables and numbers).

### Example 2:

Simplify this expression. $$12 \ – \ 3 \ x^{2} \ + \ 5 \ x \ + \ 4 \ x^{2}=$$?

Solution:

Combine “like” terms. $$- \ 3 \ x^{2} \ + \ 4 \ x^{2}=x^{2}$$
Then: $$12 \ – \ 3 \ x^{2} \ + \ 5 \ x \ + \ 4 \ x^{2}$$ $$=12 \ + \ x^2 \ + \ 5 \ x$$. Write in standard form (biggest powers first): $$x^2 \ + \ 5 \ x \ + \ 12$$

### Example 3:

Simplify this expression. $$(10x+2x+3)=$$?

Solution:

Combine “like” terms. Then: $$(10x+2x+3)=12x+3$$ (remember you cannot combine variables and numbers).

### Example 4:

Simplify this expression. $$12-3x^2+9x+5x^2=$$?

Solution:

Combine “like” terms: $$-3x^2+5x^2=2x^2$$
Then: $$12-3x^2+9x+5x^2=12+2x^2+9x$$. Write in standard form (biggest powers first): $$2x^2+9x+12$$

## Exercises

### Simplify each expression.

• $$\color{blue}{– 2 – x^2 – 6x^2}$$
• $$\color{blue}{ 3 + 10x^2 + 2}$$
• $$\color{blue}{ 8x^2 + 6x + 7x^2}$$
• $$\color{blue}{5x^2 – 12x^2 + 8x }$$
• $$\color{blue}{– 2(4 – 6x) – 3x }$$
• $$\color{blue}{ 9 – 2x + 5x + 2}$$

• $$\color{blue}{– 7x^2 – 2}$$
• $$\color{blue}{10x^2 + 5}$$
• $$\color{blue}{15x^2 + 6x}$$
• $$\color{blue}{– 7x^2 + 8x}$$
• $$\color{blue}{9x \ – 8 }$$
• $$\color{blue}{3x \ + 11}$$